15. The area of a triangle is given by
A = 1/2bh, where b is the base and h is the height of the triangle. In the triangle PQR above, PR=6, PQ=7, QR=12, and PH=3. If PH is perpendicular to QR, what is the area of the triangle PQR?
(A) 12
(B) 18
(C) 36
(D) 42

Hello! So...

We are given the following:

[tex](5-9i)-(2-6i)+(3-4i)[/tex]

_____________________________________________

1. Simplify the given expression.

[tex](5-9i)-(2-6i)+(3-4i)=5-9i-(2-6i)+3-4i[/tex]

_____________________________________________

2. Group the like terms.

[tex]-9i-4i(-2-6i)+5+3[/tex]

_____________________________________________

3. Add similar elements ( [tex]-9i-4i=-13i[/tex] ).

[tex]=-13i-(2-6i)+5+3[/tex]

_____________________________________________

4. Add the numbers ( [tex]5+3=8[/tex] ).

[tex]-13i-(2-6i)+8[/tex]

_____________________________________________

5. Remove the parentheses ( [tex]-(a+bi)=-a-bi[/tex] ).

[tex]-13i+-2-(-6)i+8[/tex]

_____________________________________________

6. Group the like terms.

[tex]-13i-(-6)i-2+8[/tex]

_____________________________________________

7. Add similar elements ( [tex]-13i-(-6)i=-7i[/tex] ).

[tex]-7i-2+8[/tex]

_____________________________________________

8. Add the numbers ( [tex]-2+8=6[/tex] ).

[tex]-7i+6[/tex]

_____________________________________________

9. Rewrite in standard complex form.

[tex]6-7i[/tex]

^Hence, our solution.

_______________________________________________________

Hope this helps! If so, lmk! If you need anything else, feel free to comment below and I'll see what else I can do to assist you further. But for now, thank you for your time and good luck!

The expression to represent the number of tomato plants he planted this year  1 / 5 x  + 6.

This year Nelson planted 6 more than one fifth of the tomato plants he planted last year.  

The expression that can be used to represent the number of tomato plant he planted this year can calculated as follows:

Therefore,

let

x = number of tomato he planted last year.

Hence, the final expression is as follows:

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:\texttt{real roots : 2 }[/tex]

[tex]\qquad \tt \rightarrow \: imaginary \: \: roots = 1[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The given polynomial is a 3rd degree polynomial so it has a total of three roots.

And we know, where the curve (of polynomial) cuts the x - axis is its real root. so, from the graph we can infer that the given polynomial has 2 real roots [ as it cuts the x - axis at two points, i.e x = -2 and x = 1 ]

Hence, Number of real roots = 2

Number of imaginary roots = total roots - real roots

i.e 3 - 2 = 1

So, number of imaginary roots = 1

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Prism is the mathematical model with different dimensions but same volume.

As given in the question,

Mathematical model represent different dimensions but same volume.

Prism is the mathematical model with different dimensions but same volume.

To prove it consider two different dimensions of prism.

Prism 1

length = 4cm

Width = 4cm

Height = 4cm

Surface area of the prism1 = 2( 4×4 + 4×4 +4×4)

                                            = 2(48)

                                            = 96cm²

Volume of prism1 = 4×4×4

                             = 64cm³

Prism 2

length = 8cm

Width = 2cm

Height = 4cm

Surface area of the prism1 = 2( 8×2 + 2×4 +4×8)

                                            = 2(56)

                                            = 112cm²

Volume of prism1 = 8×2×4

                             = 64cm³

Therefore, prism is the mathematical model with different dimensions but same volume.

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Step-by-step explanation:

i2o2k2wkekekekk2k2o2o2o2o2o292

Correct Unit rate is 4 pounds per gallons.

An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate. A unit rate is a ratio between two separate units with one as the denominator. Examples include miles/hour, kilometers/hour, meters/sec, salaries/month, etc.

Given Data

[tex]\frac{1}{4}[/tex] pounds = [tex]\frac{1}{16}[/tex] gallons

Rate = [tex]\frac{1}{4}[/tex] pounds ÷ [tex]\frac{1}{16}[/tex] gallons

Rate = [tex]\frac{1}{4}[/tex] × 16

Rate = 4

Unit rate is 4 pounds per gallons.

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Answer:Hence, the measure of angle whose measure is 32∘ less than its supplement is 74∘.

Step-by-step explanation:

Increasing amount = $10000

Median = Middle value = $40000

then

New median salary = $40000 + $10000 = $50000

Then answer is

OPTION C) $50-59 thousand

Answer:

D). Angle B ≈ Angle E

Step-by-step explanation:

ASA means that for the relation to be true, there not only has to be the 3 given proportionate values, but 2 have to be angles and 1 has to be a side.

Since we already have the 1 side, option 1 and 2 are voided.

Then since we already have Angle A and D option 3 is as well, so through this we know the answer is number 4 or Angle B = Angle E

Hope this helps.

slope= 1/4

y intercept= -5

Answer:

you accidentally put x+6 for the 1st part

The first four terms of the binomial series are  1,  x³/5,  (12/25)x⁶ and  respectively.

The binomial provided to us is (1+x^3)^-1/5.

To find out the first four terms of the binomial, we shall first extend the standard binomial (1+x)^n.

[tex](1+x)^n = 1 + nx + [n(n - 1)/2!] x^{2} + [n(n - 1)(n - 2)/3!] x^{3} +...[/tex]

As we can see here,

The value of x = x³,

The value of n = -1/5.

We get,

[tex](1+x^{3})^{-\frac{1}{5} } = 1 - \frac{1}{5} (x^{3} ) + [\frac{-1}{5} (\frac{-1}{5} -1)/2!]x^{6} + [\frac{-1}{5} (\frac{-1}{5} -1)(\frac{-1}{5} -2)/3!]x^{27} +[/tex]

From the expansion, we can see,

First term = 1

Second term = x³/5

Third term = (12/25)x⁶

Fourth term = (-13/125)x²⁷

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Answer:

• A(1)=4

• A(2)=8

• A(3)=13

• A(4)=17.5

Explanation:

The graph is given below:

The area, A(x) represents the area bounded by the graph, the horizontal axis, and the vertical lines at t=0 and t = x.

(a)A(1)

Area, A(1) is the area of a trapezoid in which: a=3, b=5 and h=1

(b)A(2)

.

(c)A(3)

.

(d)A(4)

We are given w^2 + 5w and we are asked to identify the terms for each of its parts.

First, let's start with w. The letter w is used to represent an unknown value. Thus, it is called a variable.

ext, 2. Here, 2 is useda as an exponent of w in the first term.

Meanwhile, 5 is used as a multiplier or a numerical coefficient of w in the second term.

Finally, the expression w^2 + 5w is

False, The product of two irritational numbers is either rational or irrational numbers.

A rational number is a number expressed in the form of p/q where p and q are integers and q should not be zero. Example: 2/5, 24

Whereas an irrational number is a number that is not rational in nature means it neither be expressed in the form of p/q nor in ratio terms. Example: √12, √3

Product of two irrational numbers: √2* √2 = 4 (which is a rational number)

Product of again two irrational numbers: √2*√3= √6 ( which is an irrational number)

Therefore, the product of two irrational numbers can be rational or irrational numbers.

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The product of two irrational numbers is an irrational number is false because it is either a rational or irrational number.

A rational number is defined as a numerical representation of a part of a whole that represents a fraction number.

It can be a/b of two integers, a numerator a, and a non-zero denominator b.

The product of two irrational numbers √3 ×√3 = 3

This is a rational number.

Again, the product of two irrational numbers: √5 ×√3 = √15

This is an irrational number.

As a result, the product of two irrational integers can be both rational and irrational.

Thus, the product of two irrational numbers is an irrational number is false because it is either a rational or irrational number.

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Answer:

f(3) = (3)4 + 2

Step-by-step explanation:

y = (3)4 + 2

y = 12 + 2

y = 14

The estimates for the average content is 0.9.

The variation in nitrogen content in the colony is 0.0036.

The average of a data set or the mean of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.

The sum of the data set is calculated as follows;

total = 0.98 + 0.83 + 0.99 + 0.86 + 0.9 + 0.81 + 0.94 + 0.92 + 0.87

total = 8.1

The estimated average of the nitrogen content  = 8.1/9 = 0.9

The deviation of each data from the mean;

= (0.98 - 0.9), (0.83 - 0.9), (0.99 - 0.9), (0.86 - 0.9), (0.9 - 0.9), (0.81 - 0.9), (0.94 - 0.9), (0.92 - 0.9), (0.87 - 0.9)

= 0.08, -0.07, 0.09, -0.04, 0, -0.09, 0.04, 0.02, -0.03

The sum of the square of each data from the mean;

= (0.08)² + (-0.07)²  + (0.09)² + (-0.04)² + (0.0)² + (-0.09)² + (0.04)² + (0.02)² + (-0.03)²

= 0.032

The variation of the data sample = (0.032)/9 = 0.0036

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Using the normal distribution and the central limit theorem, the probabilities are calculated as follows:

a) One meter stick greater than 100.17 cm: 0.1357 = 13.57%.

b) Group of 10 with mean less than 100.3: 0.1711 = 17.11%.

c) Group of 44 with mean greater than 100.08: 0.0918 = 9.18%.

d) Group of 50 with mean between 100.05 and 100.07: 0.5222 = 52.22%.

e) 92nd percentile of sample of 24: 100.09.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is given by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Considering the Central Limit Theorem, the z-score formula can be given as follows:

[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

The mean and the standard deviation of the lengths are given as follows:

[tex]\mu = 100.06, \sigma = 0.1[/tex]

For item a, we have that n = 1 and the probability is one subtracted by the p-value of z when X = 100.17, hence:

[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z = \frac{100.17 - 100.06}{\frac{0.1}{\sqrt{1}}}[/tex]

Z = 1.1

Z = 1.1 has a p-value of 0.8643.

1 - 0.8643 = 0.1357.

For item b, we have that n = 10 and the probability is the p-value of Z when X = 100.03, hence:

[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z = \frac{100.03 - 100.06}{\frac{0.1}{\sqrt{10}}}[/tex]

Z = -0.95

Z = -0.95 has a p-value of 0.1711.

For item c, we have that n = 44 and the probability is one subtracted by the p-value of Z when X = 100.08, hence:

[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z = \frac{100.08 - 100.06}{\frac{0.1}{\sqrt{44}}}[/tex]

Z = 1.33.

Z = 1.33 has a p-value of 0.9082.

1 - 0.9082 = 0.0918 = 9.18%.

For item d, we have that n = 50 and the probability is the p-value of Z when X = 100.07 subtracted by the p-value of Z when X = 100.05, hence:

X = 100.07:

[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z = \frac{100.07 - 100.06}{\frac{0.1}{\sqrt{50}}}[/tex]

Z = 0.71.

Z = 0.71 has a p-value of 0.7611.

X = 100.05:

[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z = \frac{100.05 - 100.06}{\frac{0.1}{\sqrt{50}}}[/tex]

Z = -0.71.

Z = -0.71 has a p-value of 0.2389.

0.7611 - 0.2389 = 0.5222 = 52.22%.

For item e, we have that n = 24, and the 92th percentile is X when Z = 1.405, hence;

[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]1.405 = \frac{x - 100.06}{\frac{0.1}{\sqrt{24}}}[/tex]

x - 100.06 = 1.405 x 0.0204

X = 100.09.

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Using the future value formula, it is found that the value of the account after the tenth deposit is of $26,361.59.

The future value formula is given by:

[tex]V(n) = P\left[\frac{(1 + r)^n - 1}{r}\right][/tex]

In which:

For this problem, the parameters are given as follows:

P = 2000, r = 0.06, n = 10.

Hence the value of the account will be of:

[tex]V(10) = 2000\left[\frac{(1 + 0.06)^{10} - 1}{0.06}\right][/tex]

V(10) = $26,361.59.

The complete problem is:

"Suppose that there is an account that pays 6% interest that is compounded annually. At the beginning of each year, $2,000 is deposited into the account (starting with $2,000 for the first year).

What will be the value of the account after the tenth deposit if no withdrawals or additional deposits are made?"

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We have:

And

After that, we proceed as follows:

STEP - BY - STEP EXPLANATION

zymiyas, this is the solution:

Brandon mows 1/4 an acre every 1/2 hour, therefore:

1/2 hour * 2 = one hour

1/4 * 2 = 2/4 or 1/2 an acre

Brandon will mow 1/2 an acre every hour

The graph of the line y=kx+1 given that the  point M(1,3) belongs to the line is shown below .

In the question ,

it is given that

the line y=kx+1 has point (1,3) on it ,

which means that the point (1,3) will satisfy the equation y=kx+1 .

So, substituting x=1 and y=3 , we get

3=k*1+1

3-1=k

k=2

Hence , the equation of the line becomes y=2x+1 .

On comparing the equation with point slope form of the the line, y=mx+c ,

we get , the slope of the line = 2 and y intercept of the line = 1 .

the graph of the line y=2x+1 is shown below .

Therefore , the graph of the line y=kx+1 given that point M(1,3) belongs to the line is shown below .

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Given data:

The series is 1 + 2 + 4 + 8 + 16 + 32 + ....

The given series is G.P because the common ratio for GP is,

Here, the common ratio is 2.

Sum of the first five numbers ,

Here, a is first term that is 1

r is common ratio that is 2

n is the number

Therefore, sum is given as

Thus, the sum of first five terms is 31

The correct option is (2).

The sales of the number of hammers that give the maximum revenue of 32400 is 1800

The equation of the revenue function is given as

R = 36x − 0.01x2

Rewrite the equation properly as a quadratic function

So, we have the following equation

R = 36x − 0.01x^2

Differentiate the above function

So, we have the following equation

R' = 36 - 0.02x

Set the differentiated function to 0

So, we have the following equation

36 - 0.02x = 0

This gives

0.02x = 36

Divide both sides by 0.02

So, we have

x = 1800

In (a), we have

36 - 0.02x = 0

0.02x = 36

x = 1800

Substitute x = 1800 in R = 36x − 0.01x^2

So, we have

R = 36 x 1800 − 0.01 * 1800^2

Evaluate

R = 32400

Hence, the maximum revenue is 32400

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Algebraic expression for Height of Balloon 2 = 7x and Height of Balloon 3 = x/2.

Heights reached by balloons 1, 2, 3 and 4 will be 54.73, 383.11, 27.36, 84.73 respectively.

We have the following given information as per the question

Balloon 1 reaches x m.

Balloon 2 reaches a height of 7 times balloon 1

∴ Balloon 2 reaches 7x m.

Balloon 3 reaches a height of half that of balloon 1.

∴ Balloon 3 reaches [tex] \frac{x}{2} [/tex] m.

Balloon 4 reaches a height of 30 meters more than balloon 1.

∴ Balloon 4 reaches ( x + 30 ) m.

Now As given The total height reached by all the balloons was 550 meters.

∴ Height of Balloon 1 + Height of Balloon 2 + Height of Balloon 3 + Height of Balloon 4 = 550 meter

∴ x + 7x + [tex] \frac{x}{2} [/tex] + (x + 30 ) =550

∴ 9.5x + 30 = 550

∴ 9.5x = 550 - 30

∴ 9.5x = 520

∴ x = 520/9.5

∴ x = 54.73 meter

(a) Algebraic expression to model the heights reached by balloons 2, 3 will be

Height of Balloon 2 = 7x = 7(54.73) = 383.11 meter

Height of Balloon 3 = x/2 = 54.73 / 2 = 27.36 meter

(b) The heights reached by balloons 1, 2, 3 and 4 will be as follows

Height of Balloon 1 = x = 54.73 meter.

Height of Balloon 2 = 7x = 7(54.73) = 383.11 meter

Height of Balloon 3 = x/2 = 54.73 / 2 = 27.36 meter

Height of Balloon 4 = x + 30 = 54.73 + 30 = 84.73 meter

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The difference between the depths in February and July is D. 13 feet.

From the information illustrated, it was stated that the depth of a local lake average 26 ft is represented as |−26|. In February, it measured 5 ft deep, or |−5|, and in July, it was 18 ft deep, or |−18|.

Therefore, it should be noted that the depth in July is -18.

Therefore, the difference between the depths in February and July will be:

= -5 - (-18)

= -5 + 18

= 13

Therefore, the depth is 13 feet.

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Let a be the number of hours that Brian works at Job A in one week and b be the number of hours that he works at Job B .in one week

Since Brian worked 22 hours per week and he made $148.60, we can set the following system of equations:

Subtracting b from the first equation we get:

Substituting the above equation in the second one we get:

Applying the distributive property we get:

Subtracting 134.20 from the above equation we get:

Dividing the above equation by 1.20 we get:

Substituting b=12 in a=22-b we get:

Answer: